Inelastic collision physics help

[jtw2e]

Homework Statement

Car A travels North at 35km/hr.
Car B travels East at 75 km/hr.
Mass of Car A = Mass of Car B
Cars have a perfectly inelastic collision.

Homework Equations

What is the magnitude of the velocity of the tangled mess after the collision? (km/hr)

The Attempt at a Solution

Px = PA_x + PB_x = M_B(0) + M_A(75) = 75km/hr*M_A

Py = PA_y + PB_y = M_B(35) + M_A(0) = 35km/hr*M_B

SQRT[(M_A*35km/hr)+(M_B*75km/hr)]

P_Total= 82.76km/hr*M_A

P=mv
v=P/m = (88.76km/hr*[STRIKE]M[/STRIKE]_A)/([STRIKE]M_A[/STRIKE]+M_B)


tanθ = Py/Px = (35km/hr*[STRIKE]M[/STRIKE])/(75km/hr*[STRIKE]M[/STRIKE]) = 0.4666667

tan^-1(0.46666667) = 25.01689 degrees.


I'm lost here... I have no idea how to get the mass OR velocity of the wreckage pile after the wreck... Please help. I have verified that my angle is at least correct.

 

[tiny-tim]

hi jtw2e!

(why do you keep using "STRIKE" ? )

P=mv
v=P/m = (88.76km/hr*[STRIKE]M[/STRIKE]_A)/([STRIKE]M_A[/STRIKE]+M_B)
…
I'm lost here... I have no idea how to get the mass OR velocity of the wreckage pile after the wreck... Please help. I have verified that my angle is at least correct.

I don't understand …

you know the mass is M_A + M_B, and you've found v

 

[jtw2e]

hi jtw2e!

(why do you keep using "STRIKE" ? )

I don't understand …

you know the mass is M_A + M_B, and you've found v

Hi tiny-tim,
I used strike to show that M/M = 1... i.e. those particular masses canceled. I have not found the V of the system after the collision, which is P_total/Mass_total. I haven't been able to find that value I don't know the mass of either car.

So I'm stuck with V_final = (88.76km/hr)/M_B

I have two unknowns. Somehow I have to find the mass of the cars, OR perhaps there is some other way to find the V? I tried to start a Conservation of Energy approach but since I didn't know mass for the Kinetic Energies, that didn't help.

 

[tiny-tim]

… I don't know the mass of either car …

yes you do! … the masses are the same!

 

[jtw2e]

yes you do! … the masses are the same!

Two unknowns: velocity and mass. Need a value to calculate either one. The fact that they are the same simplifies things, but I don't see how it gives me a number... such as 1500kg or 2000kg, etc...

 

[tiny-tim]

but they'll all cancel!

 

[jtw2e]

but they'll all cancel!

v=P/m = (88.76km/hr*MA)/(MA+MB)

They don't all cancel. Only one of the masses cancels. You are left dividing by the other. Are my formulas in error?

 

[tiny-tim]

v=P/m = (88.76km/hr*MA)/(MA+MB)

They don't all cancel. Only one of the masses cancels. You are left dividing by the other. If they all canceled we would be dividing by 0. Are my formulas in error?

of course they cancel …
M_A/(M_A + M_B) = M_A/(2M_B) = 1/2

 

[jtw2e]

Sorry, the number should be 82.76km/hr (can't read my own writing).

of course they cancel …
M_A/(M_A + M_B) = M_A/(2M_B) = 1/2

Even so, V = 82.76 km/hr / .5M

It's still 1/2 times some number M. That number M is what I need to find V. Otherwise all I know is V = 165.5 / M

 

[tiny-tim]

you must have missed an M somewhere

 

[jtw2e]

you must have missed an M somewhere

It's been...a very... long two weeks. ;)

Thanks for putting up with my... frustration and confusion.

 

[tiny-tim]

It's been...a very... long two weeks. ;)

actually, it's only been 2 hours!

get some sleep! :zzz:​